# Option greeks: sensitivity to 1% move

In a Black&Scholes framework how can I compute the following sensitivities:

• to 1% move in the underlying price
• to 1% move in implied volatility

I would like the greeks to tell me how many dollars I lose/gain if the underlying/implied volatility moves by 1%. In particular, I would like to calculate the delta and gamma (to 1% move in underlying price) and vega and volga (to 1% move in implied volatility).

For the vanna I would like to consider a 1% move in both underlying and implied volatility.

Can you please suggest how to modify Black&Sholes greeks and also how to compute the sensitivities numerically?

A reference would also be very welcome. Thank you.

If your spot increases by $h\%$, the price will increase by $\Delta_{rel,h}\%$ where $$\Delta_{rel,h} = \frac{C_{BS}(S(1+h),T,K,\sigma)}{C_{BS}(S,T,K,\sigma)} - 1$$ That's high school math.